Power Density

Today I’ve been thinking about “power density”, and I’ve got some questions for you.

But let’s start at the beginning!

In his 2009 talk at the Long Now Foundation, the engineer Saul Griffith made some claims that fill me with intense dread. Stewart Brand summarized the talk as follows:

The world currently runs on about 16 terawatts (trillion watts) of energy, most of it burning fossil fuels. To level off at 450 ppm of carbon dioxide, we will have to reduce the fossil fuel burning to 3 terawatts and produce all the rest with renewable energy, and we have to do it in 25 years or it’s too late. Currently about half a terrawatt comes from clean hydropower and one terrawatt from clean nuclear. That leaves 11.5 terawatts to generate from new clean sources.

That would mean the following. (Here I’m drawing on notes and extrapolations I’ve written up previously from discussion with Griffith):

“Two terawatts of photovoltaic would require installing 100 square meters of 15-percent-efficient solar cells every second, second after second, for the next 25 years. (That’s about 1,200 square miles of solar cells a year, times 25 equals 30,000 square miles of photovoltaic cells.) Two terawatts of solar thermal? If it’s 30 percent efficient all told, we’ll need 50 square meters of highly reflective mirrors every second. (Some 600 square miles a year, times 25.) Half a terawatt of biofuels? Something like one Olympic swimming pools of genetically engineered algae, installed every second. (About 15,250 square miles a year, times 25.) Two terawatts of wind? That’s a 300-foot-diameter wind turbine every 5 minutes. (Install 105,000 turbines a year in good wind locations, times 25.) Two terawatts of geothermal? Build 3 100-megawatt steam turbines every day — 1,095 a year, times 25. Three terawatts of new nuclear? That’s a 3-reactor, 3-gigawatt plant every week — 52 a year, times 25”.

In other words, the land area dedicated to renewable energy (“Renewistan”) would occupy a space about the size of Australia to keep the carbon dioxide level at 450 ppm. To get to Hansen’s goal of 350 ppm of carbon dioxide, fossil fuel burning would have to be cut to ZERO, which means another 3 terawatts would have to come from renewables, expanding the size of Renewistan further by 26 percent.

The main scary part is the astounding magnitude of this project, and how far we are from doing anything remotely close. Griffith describes it as not like the Manhattan Project, but like World War II — only with everyone on the same side.

But another scary part is the amount of land that needs to get devoted to “Renewistan” in this scheme. This is where power density comes in.

The term power density is used in various ways, but in the work of Vaclav Smil it means the number of usable watts that can be produced per square meter of land (or water) by a given technology, and that’s how I’ll use it here.

Smil’s main point is that renewable forms of energy generally have a much lower power density than fossil fuels. As Griffith points out, this could have massive effects. Or consider the plan for England, Scotland and Wales on page 215 of David MacKay‘s book Without the Hot Air:

One look at energy densities of common fuels is enough to understand while we prefer coal over wood and oil over coal: air-dried wood is, at best, 17 MJ/kg, good-quality bituminous coal is 22-25 MJ/kg, and refined oil products are around 42 MJ/kg. And a comparison of volumetric energy densities makes it clear why shipping non-compressed, non-liquefied natural gas would never work while shipping crude oil is cheap: natural gas rates around 35 MJ/m3, crude oil has around 35 GJ/m3 and hence its volumetric energy density is a thousand times (three orders of magnitude) higher. An obvious consequence: without liquefied (or at least compressed) natural gas there can be no intercontinental shipments of that clean fuel.

Power density is a much more complicated variable. Engineers have used power densities as revealing measures of performance for decades – but several specialties have defined them in their own particular ways….

For the past 25 years I have favored a different, and a much broader, measure of power density as perhaps the most universal measure of energy flux: W/m2 of horizontal area of land or water surface rather than per unit of the working surface of a converter.

Here are some of his results:

• No other mode of large-scale electricity generation occupies as little space as gas turbines: besides their compactness they do not need fly ash disposal or flue gas desulfurization. Mobile gas turbines generate electricity with power densities higher than 15,000 W/m2 and large (>100 MW) stationary set-ups can easily deliver 4,000-5,000 W/m2. (What about the area needed for mining?)

• Most large modern coal-fired power plants generate electricity with power densities ranging from 100 to 1,000 W/m2, including the area of the mine, the power plant, etcetera.

• Concentrating solar power (CSP) projects use tracking parabolic mirrors in order to reflect and concentrate solar radiation on a central receiver placed in a high tower, for the purposes of powering a steam engine. All facilities included, these deliver at most 10 W/m2.

• Photovoltaic panels are fixed in an optimal tilted south-facing position and hence receive more radiation than a unit of horizontal surface, but the average power densities of solar parks are low. Additional land is needed for spacing the panels for servicing, access roads, inverter and transformer facilities and service structures — and only 85% of a panel’s DC rating is transmitted from the park to the grid as AC power. All told, they deliver 4-9 W/m2.

• Wind turbines have fairly high power densities when the rate measures the flux of wind’s kinetic energy moving through the working surface: the area swept by blades. This power density is commonly above 400 W/m2 — but power density expressed as electricity generated per land area is much less! At best we can expect a peak power of 6.6 W/m2 and even a relatively high average capacity factor of 30% would bring that down to only about 2 W/m2.

• The energy density of dry wood (18-21 GJ/ton) is close to that of sub-bituminous coal. But if we were to supply a significant share of a nation’s electricity from wood we would have to establish extensive tree plantations. We could not expect harvests surpassing 20 tons/hectare, with 10 tons/hectare being more typical. Harvesting all above-ground tree mass and feeding it into chippers would allow for 95% recovery of the total field production, but even if the fuel’s average energy density were 19 GJ/ton, the plantation would yield no more than 190 GJ/hectare, resulting in harvest power density of 0.6 W/m2.

Of course, power density is of limited value in making decisions regarding power generation, because:

1. The price of a square meter of land or water varies vastly depending on its location.

2. Using land for one purpose does not always prevent its use for others: e.g. solar panels on roofs, crops or solar panels between wind turbines.

Nonetheless, Smil’s basic point, that most forms of renewable forms of energy will require us to devote larger areas of the Earth to energy production, seems fairly robust. (An arguable exception is breeder reactors, which in conjunction with extracting uranium from seawater might be considered a form of renewable energy. This is important.)

On the other hand, fans of solar energy argue that much smaller areas would be needed to supply the world’s power. There are two possible reasons, and I haven’t sorted them out yet:

1) They may be talking about electrical power, which is roughly one order of magnitude less than total power usage.

2) As Smil’s calculations show, solar power allows for significantly greater power density than wind or biofuels. Griffith’s area for ‘Renewistan’ may be large because it includes a significant amount of power from those other sources.

What do you folks think? I’ve got a lot of questions:

• what’s the power density for nuclear power?

• what’s the power density for sea-based wind farms?

and some harder ones, like:

• how useful is the concept of power density?

• how much land area would be devoted to power production in a well-crafted carbon-neutral economy?

and that perennial favorite:

• what am I ignoring that I should be thinking about?

If Saul Griffith’s calculations are wrong, and keeping the world from exceeding 450 ppm of CO2 is easier than he thinks, we need to know!

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62 Responses to Power Density

Those guys certainly should by applauded for looking at it from this very important yet so far ignored (at least in the mainstream) angle.

To me those numbers clearly show how completely absurd the whole idea really is. If the numbers are correct then going from 16 to 3 terawats in 25 years is simply impossible.

I wonder what the cost of all this titanic building effort would be.

Going by the very rough estimate from wikipedia, building a nuclear power plant in Florida cost $2444 to $3582 per kW (though with finance, risk and other additional costs it rises $5780 to $8071 per kW) But let’s go with $3000 per kW, 52 3GW plants a year will then add up to roughly $ half a trillion a year. And that’s only the nuclear portion – 3TW, that leaves 8.5 TW to go, if the rest costs roughly the same per TW we are somewhere close to $2 trillion a year for the next 25 years! For comparison the 09 US budget was $3.5 trillion.

But that of course assumes the prices for materials would remain as they are today which they won’t, such a massive infrastructure project would very quickly lead to shortages of all the major resources and experienced engineers which would drive the prices much higher.

All in all to me “11.5 TW of clean power in 25 years” scenario is complete science fiction.

If the numbers are correct then going from 16 to 3 terawatts in 25 years is simply impossible.

Yeah. In the first version of this blog post I made the mistake of “burying the lede” — failing to put the important story right at the top. That’s because I’ve been thinking about this stuff for a while and it’s not news to me.

But what Griffith is saying is absolutely important and utterly bone-chilling when you combine it with the concept that carbon is forever — meaning that we can’t make CO2 go away just by cutting back emissions to nothing.

We can only hope that Griffith is making a big mistake somewhere. If it is, we need to find it.

But since I haven’t found that mistake yet, I am very pessimistic about preventing climate change ahead of the fact. I believe we will be playing a very tough catch-up game later in this century, basically trying to minimize the damage of an ongoing disaster. Minimizing the damage is still a realistic and noble goal. That’s why I’m so eager to put my everything into the Azimuth Project.

Saul Griffith is equally pessimistic, as you can see from the New Yorker story quoted here.

Arrow, your post seems to start with the global problem, but then become only about the US, which is confusing, and perhaps unecessarily scary. The US doesn’t have to solve the entire problem itself, only its own share. Compared to the UK, the US seems fortunate, mainly due to low population density. The US has a similar amount of coast per person, and 8 times as much land per person, and its sunnier too.

Some rough figures for the US alone. Currently 300M people use 10Kw each for a total of 3Tw. People in rich EU countries use 5Kw. If Americans reduced their energy consumption to that level, the US would only need 1.5Tw. That may be psychologically or politically impossible but it isn’t technically or economically impossible. Lets say the US can manage on 2Tw plus a little fossil fuel. I think your 3$/w is about right for the investment in renewables. (Onshore wind is less, but it won’t make enough. The biggest contributor in the US seems likely to be concentrated solar thermal power which is currently around 2.5-4 $/w (Wikipedia).) So that is 6T$ over 25 years or 800$ per person per year. That is not economically impossible. Some people estimate the Iraq war cost 3T$. Finally, you need to account for that fact that less will be invested in fossil fuels.

In looking at those big numbers, don’t forget that of that 16TW of global energy consumption, a good bit is wasted – coal to electricity is about 50% and oil transport is about 25%. So the new (electrical) energy ACTUALLY needed is significantly less than 11.5TW.

Also, it doesn’t account for the “waste” implied by the huge consumption disparities seen for instance between US and European usages. As energy becomes more expensive (one way or another) then its use is necessarily going to be more efficient even in the US.

So all in all, I agree, the “11.5 TW of clean power in 25 years” scenario is complete science fiction.

As far as I can tell, Arrow said “All in all to me “11.5 TW of clean power in 25 years” scenario is complete science fiction” because he thought it was unachievable. You seem perhaps to be saying it’s complete science fiction because it’s unnecessary.

That would be great. But the big question is whether we can find an achievable scenario that would prevent CO2 levels from going over 450 ppm (for example).

So let’s do some calculations. Let’s suppose with Griffith that we need to drop from 16 terawatts of mostly fossil fuels to just 3.5 terawatts of fossil fuels within 25 years. You’re saying that we don’t need to fill the remaining 11.5 terawatts watts with renewable power. You’re saying we can do a bunch with energy conservation and waste reduction. Good! What sort of numbers would you suggest here?

I’m not trying to put you on the spot; I’m just desperate for answers.

It might help us to get started by looking at Joe Romm’s scenario, quoted below. In his plan, each “wedge” is a gigaton per year of carbon emissions. He aims for 3 wedges of efficiency and 1 of “World-War-II-style conservation”. The 3 wedges of efficiency correspond, he says, to 1.7-2.3 terawatts saved.

This cuts that scary figure of 11.5 terawatts down to
about 9.2-9.8 terawatts. Which is still scary. And his plan still sounds absurdly difficult to accomplish. Here it is:

In this post I will lay out “the solution” to global warming, focusing primarily on the 12 to 14 “stabilization wedges.”

I have argued that stabilizing atmospheric concentrations of carbon dioxide at 450 ppm or lower is not politically possible today, but that it is certainly achievable from an economic and technological perspective (see Part 1). I do, however, believe humanity will do it since the alternative is Hell and High Water.

It would require some 12-14 of Princeton’s “stabilization wedges” — strategies and/or technologies that over a period of a few decades each reduce global carbon emissions by one billion metric tons per year from projected levels (see technical paper here, less technical one here). The reason that we need twice as many wedges as Princeton’s Pacala and Socolow have said we need was explained in Part 1. That my analysis is largely correct can be seen here: “IEA report, Part 2: Climate Progress has the 450-ppm solution about right.”

I do believe only “one” solution exists in this sense — We must deploy every conceivable energy-efficient and low carbon technology that we have today as fast as we can. Princeton’s Pacala and Socolow proposed that this could be done over 50 years, but that is almost certainly too slow.

We’re at about 30 billion tons of carbon dioxide emissions a year — and notwithstanding the global economic slowdown, probably poised to rise 2% per year (the exact future growth rate is quite hard to project because it depends so much on what China does and how quickly peak oil kicks in). We have to average below 18 billion tons (below 5 GtC) a year for the entire century if we’re going to stabilize at 450 ppm (see “Nature publishes my climate analysis and solution“). We need to peak around 2015 to 2020 at the latest, then drop at least 60% by 2050 to at most 15 billion tons (4 billion tons of carbon), and then go to near zero net carbon emissions by 2100.

If we could do the 12-14 wedges in four decades, we should be able to keep CO2 concentrations to under 450 ppm. If we could do them faster, concentrations could stay even lower. We’d probably need to do this by 2040 if not sooner to have a shot at getting back to 350 this century. [And yes, like Princeton, I agree we need to do some R&D now to ensure a steady flow of technologies to make the even deeper emissions reductions needed in the second half of the century.]

Also, I tend to view the crucial next four decades in two phases. In phase 1, 2010 to 2030, the world finally gets serious about avoiding catastrophic global warming impacts (i.e. Hell and High Water). We increasingly embrace a serious price for carbon dioxide and a very aggressive technology deployment effort.

In phase 2, 2030 to 2050, after multiple climate Pearl Harbors and the inevitable collapse of the Ponzi scheme we call the global economy, the world gets truly desperate, and actions that are not plausible today — including widespread conservation — become commonplace (see here for a description of what that collapse might look like).

In the basic solution, I have thrown in a some extra wedges since I have no doubt that everybody will find something objectionable in at least 2 of them. But unlike the first time I ran this exercise, I have blogged on most of the solutions at length.

1/2 wedge of cellulosic biofuels for long-distance transport and what little aviation remains in 2050 — using 8% of the world’s cropland [or less land if yields significantly increase or algae-to-biofuels proves commercial at large scale].

1 of soils and/or biochar– Apply improved agricultural practices to all existing croplands and/or “charcoal created by pyrolysis of biomass.” Both are controversial today, but may prove scalable strategies.

That should do the trick. And yes, the scale is staggering.

He says the 3 wedges of efficiency correspond to “15-20 million gigawatt hours per year”. Check my math, everyone: a “gigawatt hour per year” is 114,079.553 watts, so 15-20 million gigawatt hours per year is 1.7-2.3 terawatts.

Everyone’s thinking of solar power in terms of generating electricity, and then using electricity to heat or cool things, where this might not be the most efficient process. Electric heating is especially inefficient, as is electric cooling (running a motor which generates heat to run a fan which blows air around a condenser).

Use solar energy to heat water directly and store it in an insulated reservoir; you could perhaps heat some of the water enough to generate steam. So you take the hot water and run it in a loop to heat a structure (radiant heating in floors), and use the steam to run a turbine which pumps the hot water around the circuit. For cooling, remember that the ground, six feet under, is at about sixty degrees F, so this is a source of cool air, and has been used in Mali, in Equatorial Africa, to cool rooms in mosques (see http://en.wikiversity.org/wiki/Underground_refrigerated_storage_room). Then what you’ve got left is heat for cooking, which might also be gotten from the water you heat during the day, run through a “stove” which can selectively store/radiate heat – or just use a solar cooker to heat the food. Water distillation is also easy, obviously. The idea is to avoid using electricity for all things except those you’ve absolutely got to have it for.

The sea is much bigger, so if the surface or volume can be utilised to house the energy production, it would help solve the problem of space. (Space is a big problem in India, especially land for big projects, including power stations, because all land near any water source is fertile.) But present technology does not allow too many ways of generating power which can be done at sea or undersea.

Surfaces of all buildings can be used to generate photovoltaic energy (this improves the power density). Roofs of buildings can also collect solar energy (or they can collect water — equally useful).

Is there any way to significantly improve the rate of conversion of CO2 to oxygen? Forestation, increasing algae concentrations, etc? It is not likely to be enough, but if CO2 could be converted to O2 at twice the present rate, we should get a few more years of leeway…?

Is there any way to significantly improve the rate of conversion of CO2 to oxygen? Forestation, increasing algae concentrations, etc? It is not likely to be enough, but if CO2 could be converted to O2 at twice the present rate, we should get a few more years of leeway…?

You wouldn’t need to double the amount of CO2 removed from the atmosphere by plants to completely solve the global warming. You’d only need to increase it by a small amount. Look at this diagram of the carbon cycle taken from Wikipedia:

(Click for a bigger version.)

As you’ll see, we’re putting 5.5 gigatons of carbon in the atmosphere each year. Land plants suck up about 121.3 gigatons/year… but put back in 121.6, if we count deforestation. The ocean sucks out 92… but puts back in 90. So, we wouldn’t need to change the balance of these natural processes very much, percentage-wise, to eat up 5.5 gigatons per year.

But: can you figure out how to actually achieve this? Freeman Dyson says it might just happen on its own, without us doing anything. He’s an optimist. His fallback position is to genetically engineer better trees — but he doesn’t know how. As you can see above, Joseph Romm wants to get rid of 2 gigatons of atmospheric carbon per year by ending tropical deforestation and planting new trees over an area equal to the continental US.

Planting new trees is apparently not nearly as effective as some magic trick that would make existing plants sequester more carbon. The problem, of course, is that existing plants put CO2 into the air as well as take it out: they don’t just photosynthesize, they also respire. They also die and rot. Dead plant matter releases carbon pretty fast; carbon in charcoal stays down there for centuries — hence the appeal of biochar.

Thanks for the numbers. Perhaps I should have said `double the number of converting agents’ — which is what I meant. And these numbers suggest that we do need to do even more than that, without genetically engineered super-algae.

Dyson is a lot smarter than most people, so it’s hard to classify him. He definitely is an optimist: he’s the guy who thought of the Dyson sphere, after all, so a little problem like global warming must seem pretty minor to him! In fact, I just found an article called Freeman Dyson: Optimist which is all about the question you just asked.

Over 30 years ago, he published a paper describing two ways to tackle global warming:

One: plant a lot of trees. Two, plant a lot of swamp plants and make sure they turn into peat. The calculations here are interesting, and he was working on how to solve this problem before most people started worrying about it. So, I would have trouble calling him a “climate change denier”.

However, I think he is too eager to dismiss the results of climate modellers. From the above article:

“The climate-studies people who work with models always tend to overestimate their models,” Dyson was saying. “They come to believe models are real and forget they are only models.” Dyson speaks in calm, clear tones that carry simultaneous evidence of his English childhood, the move to the United States after completing his university studies at Cambridge and more than 50 years of marriage to the German-born Imme, but his opinions can be barbed, especially when a conversation turns to climate change. Climate models, he says, take into account atmospheric motion and water levels but have no feeling for the chemistry and biology of sky, soil and trees. “The biologists have essentially been pushed aside,” he continues. “Al Gore’s just an opportunist. The person who is really responsible for this overestimate of global warming is Jim Hansen. He consistently exaggerates all the dangers.”

It’s true that people become wedded to their models — that’s always a danger in science. But it’s not very scientific to dismiss the results of many scientists without doing the hard work of finding better models which show their models are wrong. If you think biology will save the day against climate warming, find some evidence for that claim.

Unfortunately I don’t even know any numbers if we exclude both waste disposal and the worst case scenario of a nuclear meltdown.

The latter scenario had a large impact on the public opinion about nuclear power in Germany after the Tschernobyl accident, like the movie “The Day After” had on the public opinion about a nuclear war in the USA. If there is a chance that (once in 10 000 years) a nuclear meltdown would, for example, render the state of Washington uninhabitable for the next 100 000 years, how would you calculate the costs, or, in our case the power density?

(Steward Brand’s account of the state of the area around Tschernobyl in “Whole Earth Discipline” seems to be a hint that this possibility is rather nonexistent, and that flora and fauna are much more resilient to nuclear contamination than some people expected.)

I know, I should look up the numbers before I post any comments…but is there really that much percentage of earth’s surface covered by roofs and pavements that painting them white would have a significant influence on the albedo?!

BTW, the German government failed to pass a policy that would have enforced all houses to become passive houses within the next decade(s). There was too much protesting from houseowners and renters. And that’s an investment that actually pays off within a couple of years, because heating costs are a considerable cost factor for most people in Germany!

I dream about making buildings reflective, which would cut down on the air-conditioning in these parts of the world.

Clouds (esp. high clouds) increase albedo greatly. So we can use water as a coolant, and let it evaporate, thus allowing for both an increased albedo as well as heat exchange with the upper atmosphere. This does not work because water also rusts and dissolves, so no one wants to run water on open surfaces, but only through pipes.

I’m all in for that, but: buildings in Germany usually don’t have any cooling mechanisms, because it rarely gets so hot that you need one (that may change in the future…).

And these days, the Government failed to convince Germans that they should pay for an investment that cleary pays off, in the near future!

And Germany is a rich country, I, for example, could have afforded the proposed increase of my rent by 30% for a couple of years. How could we possibly convince people to pay for something that they “don’t need” and that “does not pay off”?

I gather that, in the more arid areas of the US, back in the 19th century one of the important considerations for exactly where trees were planted near houses was to provide shade and keep the dwelling habitable during the hottest part of the day. With the rise of electrical air conditioning the practice shifted to purely aesthetic placement.

Even now, smart people in hot parts of the US — like Southern California, where I live when I’m not in Singapore — like to have shade trees near their houses. And now the city of Riverside, my home town, pays for its residents to buy one shade tree per year!

Since 2005, the Golden State [= California] has required that flat commercial structures have white roofs. Next year, new and retrofitted residential and commercial buildings, with both flat and sloped roofs, will have to install heat-reflecting roofing, as part of an energy-efficient building code.

But the state has yet to pass any rules to encourage cooler pavement on its roads, which are largely coated with heat-absorbing asphalt, a cheap byproduct of oil refining.

According to Hashem Akbari, a physicist with the Lawrence Berkeley National Laboratory, a 1,000-square-foot roof — the average size on an American home — offsets 10 metric tons of planet-heating carbon dioxide emissions in the atmosphere if dark-colored shingles or coatings are replaced with white material.

Globally, roofs account for 25% of the surface of most cities, and pavement accounts for about 35%. If all were switched to reflective material in 100 major urban areas, it would offset 44 metric gigatons of greenhouse gases, which have been trapping heat in the atmosphere and altering the climate on a potentially dangerous scale.

That is more than all the countries on Earth emit in a single year. And, with global climate negotiators focused on limiting a rapid increase in emissions, installing cool roofs and pavements would offset more than 10 years of emissions growth, even without slashing industrial pollution.

Akbari’s paper, “Global Cooling: Increasing Worldwide Urban Albedos to Offset CO2,” to be published in the journal Climatic Change, was written with his colleague Surabi Menon and UC Berkeley physicist Arthur Rosenfeld, a member of the California Energy Commission. All three have been associated with the laboratory’s Heat Island Group, which has published extensive research on how roofs and pavement raise urban temperatures.

Akbari and Rosenfeld said they will mount an effort to persuade the United Nations to organize major cities to alter their roofing and pavement.

“I call it win-win-win,” Akbari said. “First, a cooler environment not only saves energy but improves comfort. Second, cooling a city by a few degrees dramatically reduces smog. And the third win is offsetting global warming.”

You’ll note that the above figure, “roofs account for 25% of the surface of most cities, and pavement accounts for about 35%”, is roughly consistent with the figure that Tim van Beek cited from Joe Romm: “pavements and roofs cover ca. 60% of the area of a town.” So maybe it’s true.

One problem is that I imagine a “city” as much bigger and more urban than a “town”.

I read the article that Romm links to, and the – not quite convincing- estimates are: about 0,17% to 2,4% of the land area is covered by towns, and pavements and roofs cover ca. 60% of the area of a town.

Perhaps the trick would be to have a north facing black roof also (in the temperate northern hemisphere); or some means of switching the roof from reflective to dissipative (day/night winter/summer); and/or to capture the heat for hot water. With insolation of 250 W/m2, an albedo change of 0.4, and 3 m2 north + south facing area per person in dense cities this would provides 300 W heating/reflection + cooling each when the sky is clear.

“One Olympic swimming pool of genetically engineered algae, installed every second” sounds like a lot… but we’ve seen here on this blog that biofuels are a lot worse than straight solar power when it comes to watts per square meter. So maybe all this algae would be a dumb idea.

• As biofuels go, algae are considered efficient collectors of solar energy. Under ideal growing conditions, yields in the range of 3–7 kilograms per square meter per year have been reported. A joint venture between ExxonMobil and Synthetic Genomics Inc. aims at getting 1.8 kilograms of fuel (oil) per square meter per year from algae. This is still just 0.9% of the incident solar energy. According to recent projections, it may be possible to grow algae at a rate of 12 kilograms per square meter per year with 30% oil content by mass. Assuming that the oil portion of the algae has the high energy density of 33 megajoule per kilogram, the resulting annual solar energy conversion efficiency of 4.2% is more than twice what’s been demonstrated so far.

• By contrast, solar power can be turned into heat energy at efficiencies of up to 70%!

• Or, electricity can be generated from solar power either by a solar-thermal process or a photovoltaic module with efficiencies in the range of 10 to 42%. This is much higher, but we also need to take production costs into account.

Good point! Earlier on this blog, Ijoy Tichy and Graham Young described how to use the weathering of the common mineral olivine to soak up carbon dioxide from the atmosphere. You can see what they said here:

Can someone help clarify the relation of the two chemical reactions being discussed here?

Namely,

CO2 + ½ Mg2SiO4 → MgCO3 + ½ SiO2

versus

Mg2SiO4 + 4 CO2 + 4 H2O → 2 Mg2+ + 4 HCO3– + H4SiO4

Are they alternative pathways, different ways of looking at what actually happens in nature, or what? You’ll see some more chemistry questions in the green box on that Azimuth Project page. I need help!

“Maybe people here will enjoy guessing the main source of error in this calculation …”

(of the price of gigatonnes of olivine)

I would say it is the fact that there are mountains of olivine, or as they are sometimes called, mountains of dunite, harzburgite (partly olivine), peridotite, and probably some others I haven’t learned.

The earth’s mantle is made of these things, and sticks through the crust in many places. Plants don’t grow on these outcroppings, and here is a nice illustration of the join with adjacent plant-supporting terrain, from http://www.alpinenz.com/Red-Hills.html.

If a coal burner put a particular mole of CO2 into the atmosphere, ~400 primary kJ were yielded. I figure olivine pulverization to 25 microns will require another 40 primary kJ, and lifting this powder 5 km into the atmosphere, 10 kJ, for a total of one-eighth of the long-ago energy that now must be spent to clean up after it.

My idea is to let the wind spread out these slowly settling particles. Lifting them higher would help, but 5 km is about as far as a stream launched from the ground can climb without being initially supersonic. I foresee this large air-cleaning job being done from large central plants, built on olivine terrain, that won’t do anything else; maybe they’ll be able to have tall launch towers so as to get more height without exposing the stream to air drag at first.

The market value of olivine is $50 to $100 per ton depending on quality. Plugging in the larger numbers then 5 trillion dollars a year would adsorb all the co2 we produce.

John wrote:

Maybe people here will enjoy guessing the main source of error in this calculation…

G. R. L. wrote:

I would say it is the fact that there are mountains of olivine, or as they are sometimes called, mountains of dunite, harzburgite (partly olivine), peridotite, and probably some others I haven’t learned.

Maybe, but here’s my guess: ppnl took the current-day price of olivine (say $100/ton) and multiplied it by the amount needed to deal with all the CO2 produced each year (about 48 gigatons) to arrive at a cost of about 5 trillion dollars/year.

But this neglects economic effects like the law of supply and demand: if we suddenly placed an order for 48 gigatons of olivine, the price would skyrocket, since that vastly exceeds — doubtless by many orders of magnitude — the amount mined now!

Indeed right now the price would be infinite, since there’s no way we could buy this much olivine until production got ramped up.

Later, things would change. For example, people might start scraping it off mountaintops. But it would take real work to predict the cost of such large-scale production.

Serpentine is about 10 times more abundant than olivine. A ton of serpentine can dispose about two-thirds of a ton of CO2; this reaction is exothermic and yields about 64 kilojoules/mole. The problem is getting to happen fast and figuring out how to take advantage of the energy released! A team of US researchers is making progress on this — check out the link for details.

There seems to be too much concern over the rate of the reaction as far as I can tell. I saw an abstract of a paper that suggested that just spreading the minerals over the ground is sufficient. The reaction may be slow but with a large enough area it will absorb a large amount of carbon. Its low tech and simple.

Also putting the ground up mineral in the ocean may counter ocean acidification. The ocean cycles huge amounts of co2 out of and into the atmosphere. Use the ocean as a massive reaction vessel and the rate of reaction is not very important.

The only use I can see for the fast reaction rates is to absorb point sources of co2 like in a clean coal power plant or coal gasification.

I saw an abstract of a paper that suggested that just spreading the minerals over the ground is sufficient.

A link to that would be much appreciated!

Supposedly it takes about a year for these minerals to weather if they’re ground up and put someplace where they get air and also rainwater. At least this is the figure for olivine; for now I’ll assume serpentine works similarly.

A year is not bad. The problem is convincing someone to grind up vast amounts of rock and spread it thinly enough so that it gets air and rainwater — or maybe dump it in the ocean.

How vast, exactly?

A ton of serpentine can get rid of about two-thirds of a ton of CO2. According to Wikipedia, in 2008 about 31.8 gigatons of CO2 were emitted from fossil fuels (and more from land use change). So, to counter that we’d need to grind up and disperse about 48 gigatons of serpentine a year.

For comparison, total world cement production in 2009 was about 2.8 gigatons. The total amount of material handled by US mines in 2008 was about 5.6 gigatons. (I don’t see worldwide figures on that.)

So, I think it would be a challenge getting people to grind up and spread around 48 gigatons of rock each year. One advantage of doing it in some sort of plant, at a higher reaction rate, is that the energy produced by this reaction can be captured. But I don’t know if this could become a commercially interesting way of generating power — even after legislation greatly raises the price of CO2 emissions. It might; I just don’t know.

The energy cost of moving the rock around and grinding it up would be high. Neither is it easy to utilise the heat.

“Although many carbonation reactions are exothermic, it is generally very difficult to recover the low-grade heat while the long reaction time and demanding reaction conditions contribute to process expense.” Philip Goldberg1 et al.

The suggestion has been made elsewhere that the reaction will take place reasonably completely at fairly high temperature underground if the rock is first cracked. The heat of reaction then cracks the rock more thus exposing fresh surface area. Presumably geothermal energy could then be extracted. But at the necessary scale, would this be safe and where could it be done without high environmental costs?

The market value of olivine is $50 to $100 per ton depending on quality. Plugging in the larger numbers then 5 trillion dollar a year would adsorb all the co2 we produce. Very expensive but doable in the extreme.

I don’t know how much cheaper it could be done. And it isn’t clear what the carbon footprint of all that activity would be.

Wherefore all this talk of “replacing” power-output? Sure, twitter is fun (though I don’t tweet, myself), and I’m glad of the global telephone network (at least where there are emergency services), but how much of this power usage is *necessary*? How much of it is *sensible*?

What, for instance, is the energy cost of a google search, from *running* the hardware to *replacing* it? If they get faster, does that translate into reduced power consumption or increased? How about on-demand video? Is this, energy-wise, cheaper than scheduled broadcast? And do we really need it?

It’s undoubtedly a complicated multidimensional problem, and there are probably other variables as well as just the “total energy used”. For instance, there are the stories in the UK in the 70s and 80s (before the UK media fragmented in the 90s) of power plants being specially brought online to cope with the “popular TV program break where everyone boils an electric kettle” demand spike. To some extent, using renewables such as wave and wind you really want to avoid demand spikes more than to reduce the total load.

2) what is an estimate of the maximum installation rate, keeping the actual number of producers ? (e.g. max installation rate < max production rate)

3) what is the average lifetime of the three items above ?

4) what is the production+installation cost of the 3 items above ?

I think #3 and #4 (actually #4/#3) are especially important to assess which one, among the renewable energy sources, is the most viable.

Items #1 and #2 would get a sense of the time needed to actually build Renewistan, which i don't think can be done in less than 100 years, which is too late to prevent warming, but it just might be in time for when we run out of oil, coal, gas and uranium.

Good questions Giampiero! I would love to spend all day answering them, but I just tackled olivine and serpentine weathering to soak up CO2, albedo reduction by painting rooftops white, and the comparison of algae biofuels to solar power… and I promised myself to work on a math paper that’s due next week!

So, here are my only contributions now to answering your questions. Finding this out took 3 minutes:

• According to this site, “In 2005, 1,460 megawatts of PV were installed. This increased to 1744 megawatts in 2006.”

• According to the same site, in 2001, the cumulative installed photovoltaic solar power in a bunch of countries was 1000 megawatts.

After scratching my head for 3 more minutes, I realized that when they said “In 2005, 1,460 megawatts of PV were installed”, they did not mean that this much was newly installed in 2005. This must be a cumulative figure!

At least I think so — it’s confusingly worded.

So, if I’m interpreting it correctly, roughly 300 new megawatts of photovoltaics were installed in the year of 2005.

This isn’t nearly good enough: Griffith wants us to install 2 terawatts of photovoltaics in 25 years, and Romm wants us to do the same by 2040. If we give ourselves 30 years, this is roughly 70,000 new megawatts of photovoltaics per year.

Sounds really bad. But the rate of installation is growing exponentially at a substantial rate. According to that same site, the total amount of installed photovoltaics has been going up 20-25% per year.

Do we have a chance? Someone here can do the calculation with the data I just gave! Someone here can find newer, better data!

Taking into account that “capacity is expected to double every 16 months over the next five years”, that would amount to roughly 6000 new MW of CSP in 5 years, which means a rate of 1200 new MW at year. Better but still a far cry from the 70000 MW / year required to have 2TW of CSP in 25years (it will take more than a 1K years at this rate).

It is interesting also that Hydro and Geothermal score slightly better than wind. This makes me wonder if perhaps we should include geothermal in the list of serious renewables. (Any thoughts on this ?)

WIND:http://www.wwindea.org/home/index.php
“38312 MW of Wind Power were added in 2009”. It’s not bad at all (actually maybe too good to be true), meaning we could actually reach 2TW from wind in less 50 years at this rate.

LIFETIME: i keep on running into estimates of 25-30 years lifetime for PV, CSP, and Wind Turbines. I still think plant lifetime might be the most important piece of the puzzle though.

GEOTHERMAL: from Wikipedia, “10,715 megawatts (MW) of geothermal power in 24 countries is online in 2010. This represents a 20% increase in online capacity since 2005.”
This means an addition rate of 357MW/year.

Well, back of the envelope: google says 1.25^30 = 807.793567. Let’s say that’s about 1000. So after 30 years, with a 25% increase per year, we’re at 300 megawatts * 1000 or 300 gigawatts. That’s about 1/7 of the 2 terawatt target.

On solar installations I know some of volunteers I am familiar with who formed a NGO to try to fund some local school solar demonstration project. The initial capital cost was formidable. Later I got the word that one local school got funding for solar based on local bond measures. There were also solar installations funded by the Recovery Bill in other locations.

So I have some local deployments that are not density constrained, but capital cost constrained, plus an example how that was worked around.

2) As I mentioned by email a few weeks back I think John Cook’s “Skeptical Science” would make a worthy addition to the blogroll (respectable folk can respond to climate denialists and delusionals more time-effectively by referring them to the talking-point refutations in John’s list).

3) Bear in mind that big numbers dealing with things of the scale of Earth’s dimensions and total human population are always big, not only when they’re anthropocentric or energy economy things. The gross amount of energy that could be saved were each of us to eat less meat and drive smaller cars and ride more bikes and holiday closer to home and live in welldesigned homes needing less aircon and lit by smarter bulbs, and so on … is a really impressive number.

4) The 25 year time frame mooted here in your discussion is of the order of a coal power plant lifetime. If the price of carbon today were made high enough, with promise of further rises to come, then little more investment in coal power would be made and we would almost naturally find ourselves in 25 years time with few to no coal burning power stations left.

Motor vehicles are easier to do because their typical lifespan is of order only 10 years. To replace oil-burners almost entirely within 25 years should be quite manageable, particularly as current engine technologies already burn various biofuels about as well as they burn gasoline. 25 years ought to be plenty of time to replace oil as a fuel.

5) Freeman Dyson has the gall of a prof emeritus to patronize people doing work he doesn’t understand as “alarmists”.

Also, getting your name attached to something does not always mean you came up with the original idea:

Not only was every solar system now surrounded by a gauze of light traps, which focused the escaping solar energy for intelligent use, so that the whole galaxy was dimmed, but many stars that were not suited to be suns were disintegrated, and rifled of their prodigious stores of sub-atomic energy”.

But I come not to bury Freeman Dyson but to ignore him on the subject of things he not only doesn’t understand, but doesn’t understand that he doesn’t understand and doesn’t have the modesty to shut up about.

6) Most of these questions of an evolution from fossil fuels are more matters of economics than science or technology. Does anyone doubt that had we begun running out of coal and oil in the 60s that we’d have replaced them by now in our energy economy as and where necessary? Going back just four generations we even replaced cheap grass-burning ponies with more expensive automobiles. With tax incentives today to move away from fossil fuels – we should be taxing “bads” like coal and simultaneously alleviating taxes on “goods” such as people’s income – we could quite possibly be improving our economies while putting the embarrassing dinosaur energy era behind us.

the trouble with ponies and horses is their exhaust, so to speak. If we used horses for personal transport now, most of our cities would be neck-deep in horse manure. And then there’s the problem of disposing of dead horses… Both of those things were significant problems four generations ago.

I hate to suggest that it’s more complicated than “economics will automatically handle it”, but the evidence in the UK suggests that people don’t respond to tax “incentives” in the smooth way. The already high (by global standards) tax on petrol (gasoline) increased by 8.7 percent between 2000 and 2010, at a time when incomes and inflation in the UK weren’t increasing much. Over the same time period private car miles driven (admittedly extrapolated from sampling, so possible issues) increased by 4.5 percent in the same time. This is not what theoretical economists argue should happen in the presence of taxes.

Talking to general people here in the UK (not enivronmentalists) the attitude seems to be “The cost really hurts, but I’ll drive until the cost is postively ruinous”, not “I’ll try and start to find alternatives to reduce usage”.

We’re simple creatures David so keeping things as simple as possible can be wise policy; when things get complicated most of us tend to become a little bit confused.

A carbon tax is certainly a simple idea (the implementation details and political arguments around it less so) and it’s championed these days by many world-class economists of varying ideological flavours – see an honor roll at the Pigou Club http://en.wikipedia.org/wiki/Pigou_Club

We tend to defer to the advice of specialists when out of our own areas of expertise on matters like climate science, so I think it’s not too silly on occasion to listen to smart economists on subjects in their own field. Some have been proposing a carbon tax for a long while now, Bill Nordhaus since 1976 (Greg Mankiw’s listing of him as current only as of 2006 at the Pigou Club is a bit of cheek, really).

At the street level that you mention, apart from as you suggest making people think harder about how much they want to be burning fuel in their cars, a carbon tax also tends to make alternative non-fossil fuels more cost-competitive and encourages people to look for greater fuel efficiency, perhaps buy smaller cars, turn some of them into inventors and technology entrepreneurs, and so on. The tax is a simple thing but because it goes to the nub of the problem – that burning fossil carbon has been cheap and easy yet environmentally ruinous – it can have more than the one, simple, good effect.

I’m inclined to the opposite position: human minds are bizarre, incredibly complicated things with all sorts of conflicting beliefs at the same time (some of the results of behavioural economics and related psychology experiments show this). In particular, there seem to be a lot of observed cases where the predictions of economists using certain axioms and models are not borne out. It’s even interesting that you support the Pigou club by talking about the ideological varieties of the economists who support it rather than, say, their “predictive success” or “observational commitment”.

I don’t oppose a carbon tax, indeed I think it would be a good thing. But I don’t think it’ll be more than a very minor contributor to changing behaviour patterns of people and companies: I think technology development motivated by “environmental concerns” and psychological changes in consumer behaviour will have a much bigger effect. As the evidence I quoted suggests, people find ways to ignore the effects of increased taxes when they conflict with what they currently want to do.

The author of the article you cite admits that we’ll need to work wonders:

Innovations in nanotechnology and
other advances in materials science
would make it possible to transform our
vision of plentiful, low-cost energy into a
reality. By developing new technologies,
marshaling the excellent resources of
organizations like the Materials Research
Society, and developing the talents of a
new generation of scientists and engineers,
I believe that we can solve even
our most critical energy problems.

Dear Giampero – I’m very glad you’ve been doing some calculations, and I want to return to discussing this subject, especially now that I’ve found some “professional” work on this subject which we should analyze! I will write about that in a new post.

So, according to this 2008 article 100 new MW of CSP (Concentrating Solar Power) were installed in 2007.

Taking into account that “capacity is expected to double every 16 months over the next five years”, that would amount to roughly 6000 new MW of CSP in 5 years, which means a rate of 1200 new MW a year. Better but still a far cry from the 70000 MW / year required to have 2TW of CSP in 25 years (it will take more than a 1K years at this rate).

I agree that it looks hopeless.

But I must note that you are assuming the amount of new concentrated solar power (=CSP) installed per year levels off in 2012 at the rate of 6000 MW/year. Why can’t it keep growing?

Just for fun, let us make the very optimistic assumption that new CSP keeps doubling every 16 months, starting in 2007. What will we see 25 years later?

25 × 12/16 = 18.75 so it will have doubled 18.75 times by then.

218.75 is about 440,000, so it will grow by this factor.

In other words, starting from 100 megawatts/year of new concentrated solar power in 2007, we’ll be getting 44,000,000 megawatts/year of new CSP 25 years later. Or in other words, 44 terawatts/year!

That would be great: it would come late, but come in large amounts.

However, this calculation assumes a continued exponential growth without any reason to think that is practical.

(Someone should also check my math; it’s easy to make enormous, embarrassing mistakes.)

I have seen another estimate, which some call optimistic, saying that total wind and solar electrical power generation might be around 1 terawatt by 2030 and 5 terawatts by 2100. That’s vastly worse.

My plan is to figure out realistic values of these numbers, with the help of everyone here. For these more realistic calculations I will need to do something much more intelligent than extrapolate an exponential function. All the factors you mention will become important.

As a late addition to this post I wanted to point out some recent work on well placed vertical axis wind turbines. See, e.g., http://arxiv.org/abs/1002.2250 on the theoretical side of things and http://arxiv.org/abs/1010.3656 on the experimental, both by the same group. Though the research seems in its infancy there are some interesting ideas and power densities approaching 100 W/m^2 suggest its well worth further investigation.

How To Write Math Here:

You need the word 'latex' right after the first dollar sign, and it needs a space after it. Double dollar signs don't work, and other limitations apply, some described here. You can't preview comments here, but I'm happy to fix errors.